Synchronization for fractional FitzHugh-Nagumo equations with fractional Brownian motion

摘要

This paper is devoted to dynamics of the Caputo-type fractional FitzHugh-Nagumo equations (FHN) driven by fractional Brownian motion (fBm). The existence and uniqueness of mild solution for of the Caputo-type fractional FHN are established, and the exponential synchronization and finite-time synchronization for the stochastic FHN are provided. Finally, the numerical simulation of the synchronization for time-fractional FHN perturbed by fBm is provided; the effects of the order of time fractional derivative and Hurst parameter H$$ H $$ on synchronization are also revealed.